Digital PSAT Math Practice Question 267: Answer and Explanation

Question: 267

9a² - 81b² is equivalent to which of the following expressions?

• A. (3a + 3b)(3a - 3b)
• B. 3(a - b)(a + 3b)
• C. 9(a + 3b)(a - 3b)
• D. 9(a - 3b)(a - b)

Correct Answer: C

Explanation:

(C) First, you can factor out a 9:

9(a² - 9 b²)

Something of the form (x² - y²) is a difference of perfect squares and factors to (x + y)(x - y). In this case, x = a, while y = 3b since (3b)² = 9b². Therefore, a² - 9b² = (a + 3b)(a - 3b). Remembering the 9 you previously factored out gives you 9(a + 3b)(a - 3b), choice (C).

Alternatively, you could have FOILed all answer choices to see which choice gave you the expression in the question's statement.